Wittmann, Flood, and Black on embodiment in separating variables

Algebraic manipulation as motion within a landscape
Michael C. Wittmann, Virginia J. Flood, Katrina E. Black
Educational Studies in Mathematics
February 2013, Volume 82, Issue 2, pp 169-181

We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landscape, capable of being moved around. We analyze our results within the tradition of embodied cognition and use conceptual metaphors such as the path-source-goal schema and the idea of fictive motion. We find that students solving the problem correctly and efficiently do not use overt mathematical language like multiplication or division. Instead, their gestures and ambiguous speech of moving are the only algebra used at that moment.

Harrer, Flood, and Wittmann on Energy in middle school science

Students talk about energy in Project-Based Inquiry Science
Benedikt W. Harrer, Virginia J. Flood, and Michael C. Wittmann
AIP Conf. Proc. 1513, 162 (2013)

We examine the types of emergent language eighth grade students in rural Maine middle schools use when they discuss energy in their first experiences with Project-Based Inquiry Science: Energy, a research-based curriculum that uses a specific language for talking about energy. By comparative analysis of the language used by the curriculum materials to students’ language, we find that students’ talk is at times more aligned with a Stores and Transfer model of energy than the Forms model supported by the curriculum.

Kaczynski and Wittmann on expectations about damped harmonic motion

Student expectations in a group learning activity on harmonic motion
Adam Kaczynski and Michael C. Wittmann
AIP Conf. Proc. 1513, 210 (2013)

Students in a sophomore-level mechanics course participated in a new group learning activity that was intended to support model-building and finding coherence between multiple representations in the context of an underdamped harmonic system. Not all of the student groups framed the activity in the same way, and many attempted tasks that existed outside of the prompts of the activity. For one group, this meant that instead of providing a rich verbal description, they framed the activity as finding a mathematical expression.

Wittmann and Hawkins on new versions of FMCE questions

New ways of investigating the canonical coin toss acceleration problem
Michael C. Wittmann and Jeffrey M. Hawkins
AIP Conf. Proc. 1513, 422 (2013)

Asking students about the acceleration of a tossed object is a well-studied problem in physics education research. Students frequently respond using reasoning that describes the velocity of the object, in particular that acceleration is zero at the top. We created new versions of the canonical multiple-choice Force and Motion Conceptual Evaluation coin-toss questions to investigate what other reasoning students might use. Some students were asked “is the acceleration zero at the top?” Other students were told “the acceleration is not zero” and asked to explain. A third group answered the original multiple-choice version of the question. Our results suggest that some students give answers that they can explain are incorrect. We also find that some students’ responses about the acceleration at the turnaround point are affected by question format.

Chase and Wittmann on Embodied Cognition

Evidence of embodied cognition via speech and gesture complementarity
 Evan A. Chase and Michael C. Wittmann
 AIP Conf. Proc. 1513, 94 (2013)

We are studying how students talk and gesture about physics problems involving directionality. Students discussing physics use more than words and equations; gestures are also a meaningful element of their thinking. Data come from one-on-one interviews in which students were asked to gesture about the sign and direction of velocity, acceleration, and other quantities. Specific contexts are a ball toss in the presence and absence of air resistance, including situations where the ball starts at greater than terminal velocity. Students show an aptitude for representing up to 6 characteristics of the ball with 2 hands. They switch quickly while talking about velocity, acceleration, and the different forces, frequently representing more than one quantity using a single hand. We believe that much of their thinking resides in their hands, and that their gestures complement their speech, as indicated by moments when speech and gesture represent different quantities.

Hawkins, Frank, Thompson, Wittmann, and Wemyss on alternative question strategies

Probing student understanding with alternative questioning strategies
Jeffrey M. Hawkins, Brian W. Frank, John R. Thompson, Michael C. Wittmann, and Thomas M. Weymss
AIP Conf. Proc. 1413, 207 (2012)

Common research tasks ask students to identify a correct answer and justify their answer choice. We propose expanding the array of research tasks to access different knowledge that students might have. By asking students to discuss answers they may not have chosen naturally, we can investigate students' abilities to explain something that is already established or to disprove an incorrect response. The results of these research tasks also provide us with information about how students' responses vary across the different tasks. We discuss three underused question types, their possible benefits, and some preliminary results from an electric circuits pretest utilizing these novel question types. We find that the answer students most commonly choose as correct is the same choice most commonly eliminated as incorrect. Also, given the correct answer, students can provide valuable reasoning to explain it, but they do not spontaneously identify it as the correct answer.

Wittmann and Black on integration and separation of variables

When basic changes to a solution suggest meaningful differences in mathematics
Michael C. Wittmann and Katrina E. Black
AIP Conf. Proc. 1413, 93 (2012)

When solving two integrals arising from the separation of variables in a first order linear differential equation, students have multiple correct choices for how to proceed. They might set limits on both integrals or use integration constants on both or only one equation. In each case, the physical meaning of the mathematics is equivalent. But, how students choose to represent the mathematics can tell us much about what they are thinking. We observe students debating how to integrate the quantity dt. One student seeks a general function that works for everyone, and does not wish to specify the value of the integration constant. Another student seeks a function consistent with the specific physics problem. They compromise by using a constant, undefined in value for one student, zero in value for the other.

Harrer, Scherr, Wittmann, Close and Frank on proximal formative assessment about energy

Elements of proximal formative assessment in learners' discourse about energy
Benedikt W. Harrer, Rachel E. Scherr, Michael C. Wittmann, Hunter G. Close, and Brian W. Frank
AIP Conf. Proc. 1413, 203 (2012)

Proximal formative assessment, the just-in-time elicitation of students' ideas that informs ongoing instruction, is usually associated with the instructor in a formal classroom setting. However, the elicitation, assessment, and subsequent instruction that characterize proximal formative assessment are also seen in discourse among peers. We present a case in which secondary teachers in a professional development course at SPU are discussing energy flow in refrigerators. In this episode, a peer is invited to share her thinking (elicitation). Her idea that refrigerators move heat from a relatively cold compartment to a hotter environment is inappropriately judged as incorrect (assessment). The "instruction" (peer explanation) that follows is based on the second law of thermodynamics, and acts as corrective rather than collaborative.

Wittmann and Chase on embodied cognition in wave propagation

Evidence of embodied cognition about wave propagation
Michael C. Wittmann and Evan Chase
AIP Conf. Proc. 1413, 383 (2012)

That students think of wavepulses as if throwing balls down a long taut spring is well established. Typical questions involve students imagining the spring already pulled taut; a different scenario would imagine them pulling the spring tight first. This situation creates a different baseline of physical experience from which to reason. For example, it provides a physical experience in which tension is a relevant measure in the system. We investigated the effects of students pulling the spring (or not) in interviews after instruction. We also wrote two surveys, each giving a different physical description of a typical problem. From interviews, we find evidence that a different embodiment of the problem affects students' responses. In surveys, with students asked to imagine different situations, we found no such evidence.

Christensen and Thompson on graphical slope and derivative representations

W.M. Christensen and J.R. Thompson
Investigating graphical representations of slope and derivative without a physics context
Phys. Rev. ST Physics Ed. Research 8, 023101 (2012).
http://link.aps.org/doi/10.1103/PhysRevSTPER.8.023101

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a physics context. As an extension from this work on students’ mathematical competency at the upper level in physics, we report on a preliminary investigation of mathematical understanding of fundamental concepts of slope and derivative among students in a third- semester multivariable calculus course. Among the first published findings of physics education research are investigations on students’ understanding of kinematics, with particular attention to graphical representations of position-, velocity-, and acceleration-versus-time graphs. Underlying these physical quantities are relationships that depend on derivatives and slopes. We report on our findings as we attempt to isolate students’ understanding of these mathematical concepts.

Thompson Christensen Wittmann on graduate course in PER

John R. Thompson, Warren M. Christensen, Michael C. Wittmann

Preparing future teachers to anticipate student difficulties in physics in a graduate-level course in physics, pedagogy, and education research

We describe courses designed to help future teachers reflect on and discuss both physics content and student knowledge thereof. We use three kinds of activities: reading and discussing the literature, experiencing research-based curricular materials, and learning to use the basic research methods of physics education research. We present a general overview of the two courses we have designed as well as a framework for assessing student performance on physics content knowledge and one aspect of pedagogical content knowledge—knowledge of student ideas—about one particular content area: electric circuits. We find that the quality of future teachers’ responses, especially on questions dealing with knowledge of student ideas, can be successfully categorized and may be higher for those with a nonphysics background than those with a physics background.

URL: http://link.aps.org/doi/10.1103/PhysRevSTPER.7.010108
DOI: 10.1103/PhysRevSTPER.7.010108
PACS: 01.40.J-

Casey Murphy MST: Interaction and MPEX analysis of group learning behaviors

Casey Murphy
Answer-Seeking and Idea-Constructing During Collaborative Active-Learning Activities in a Physics Laboratory
Unpublished MST thesis, University of Maine, 2010

Students’ understanding of the nature of scientific knowledge and their sense of self-efficacy in the construction of scientific ideas impacts their approach to learning in a physics laboratory (Hammer, 1995). This research uses video analysis to explore two polar examples of group epistemological approach within the same laboratory. One group seemed to approach the activities with the goal of answer-seeking, often at the expense of meaningful learning, while the other group seemed to actively engage in idea- construction as they worked through the instructional sequence. Using methods of Interaction Analysis (Jordan & Henderson, 1995), I describe very different behavioral patterns for each group across three spheres of interaction - student interactions with group members, student interactions with space and time, and student interaction with authority. These results suggest that it is possible to assess students’ approaches to a laboratory by being attentive to what students say and do as they interact with group members, with the space around them and with authority. The emergent patterns could provide the basis of a teacher toolbox for gauging, whether or not student approach is matched to the intended epistemological goals of the course.

In addition to looking at the details of behavior in the classroom, I explored shifts in epistemological approach to physics learning from the beginning of the course to the end of the course with the Maryland Physics Expectation Survey (MPEX2) (McCaskey, 2009). Consistent with previous semesters, whole course results indicated no shift towards favorability in personal or epistemological independence between pre- and post- tests. I also analyzed student survey responses at the beginning of the semester for the entire class, and, more importantly, for the Answer-Seeking Group and the Idea- Constructing Group. I observed a mismatch between behavior observed in class and student response on the MPEX2 questions measuring the extent students see knowledge as constructed or absorbed (independence-epistemology). On the other hand, I observed a match between group behaviors and the questions probing self-efficacy in knowledge construction. These results challenge earlier studies indicating low validity for MPEX2 use as an individual or small-N diagnostic (McCaskey, 2009) and also confirm analysis of the MPEX2 Independence cluster at the sub-category level of independence–personal and independence-epistemology.

Smith, Thompson, and Mountcastle on the Boltzmann Factor

Trevor I. Smith, John R. Thompson, and Donald B. Mountcastle

Addressing Student Difficulties with Statistical Mechanics: The Boltzmann Factor

AIP Conf. Proc. -- October 24, 2010 -- Volume 1289, pp. 305-308
2010 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3515230

As part of research into student understanding of topics related to thermodynamics and statistical mechanics at the upper division, we have identified student difficulties in applying concepts related to the Boltzmann factor and the canonical partition function. With this in mind, we have developed a guided-inquiry worksheet activity (tutorial) designed to help students develop a better understanding of where the Boltzmann factor comes from and why it is useful. The tutorial guides students through the derivation of both the Boltzmann factor and the canonical partition function. Preliminary results suggest that students who participated in the tutorial had a higher success rate on assessment items than students who had only received lecture instruction on the topic. We present results that motivate the need for this tutorial, the outline of the derivation used, and results from implementations of the tutorial. ©2010 American Institute of Physics

Hawkins et al. on vector addition

Jeffrey M. Hawkins, John R. Thompson, Michael C. Wittmann, Eleanor C. Sayre, and Brian W. Frank

Students' Responses To Different Representations Of A Vector Addition Question

AIP Conf. Proc. -- October 24, 2010 -- Volume 1289, pp. 165-168
2010 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3515188

We investigate if the visual representation of vectors can affect which methods students use to add them. We gave students one of four questions with different graphical representations, asking students to add the same two vectors. For students in an algebra-based class the arrangement of the vectors had a statistically significant effect on the vector addition method chosen while the addition or removal of a grid did not. ©2010 American Institute of Physics

Springuel Ph.D.: Cluster analysis in kinematics and the FMCE

Applying Cluster Analysis to Physics Education Research Data
R. Padraic Springuel, 2010

One major thrust of Physics Education Research (PER) is the identification of student ideas about specific physics concepts, both correct ideas and those that differ from the expert consensus. Typically the research process of eliciting the spectrum of student ideas involves the administration of specially designed questions to students. One major analysis task in PER is the sorting of these student responses into thematically coherent groups. This process is one which has previously been done by eye in PER. This thesis explores the possibility of using cluster analysis to perform the task in a more rigorous and less time-intensive fashion while making fewer assumptions about what the students are doing. Since this technique has not previously been used in PER, a summary of the various kinds of cluster analysis is included as well as a discussion of which might be appropriate for the task of sorting student responses into groups. Two example data sets (one based on the Force and Motion Conceptual Evaluation (FMCE) the other looking at acceleration in two-dimensions (A2D) are examined in depth to demonstrate how cluster analysis can be applied to PER data and the various considerations which must be taken into account when doing so. In both cases, the techniques described in this thesis found 5 groups which contained about 90% of the students in the data set. The results of this application are compared to previous research on the topics covered by the two examples to demonstrate that cluster analysis can effectively uncover the same patterns in student responses that have already been identified.

Recommended Citation
Springuel, R. Padraic, "Applying Cluster Analysis to Physics Education Research Data" (2010). Electronic Theses and Dissertations. 1086.
http://digitalcommons.library.umaine.edu/etd/1086